“Il più appassionatamente” and “il più raramente” are wrong. They would be technically OK if you added “possibile”, but I do think no native speaker would ever use them.

(4) They left it as late as possible before setting out on the journey
L’hanno lasciato il più tardi possibile prima di partire sul [per il ] viaggio

What does “it” refer to? It is a little ambiguous.

(5) I drove as quickly as possible to reach the railway station in time to meet Maria
Ho guidato [or: guidai] il più rapidamente (o velocemente) possibile per arrivare alla stazione ferroviaria in tempo per incontrare Maria.

I would only say “più velocemente”; you can say “il più rapidamente (o velocemente)” when using for example the verb “camminare”; means of transport usually require “velocemente”. There are exceptions, though: “Le auto della polizia giunsero rapidamente sul luogo dell’attentato.)

“Il meno spesso / stranamente / avidamente / chiaramente / precisamente” are wrong. Again, they would be technically OK if you added “possibile”, but I do think no native speaker would ever use them. See above.

However, it can just as easily appear as:
Di tutte le fotocamere questa è quella che mette a fuoco il più precisamente [possibie: but see above] OR

Dylan Thomas wrote:
(4) They left it as late as possible before setting out on the journey
L’hanno lasciato il più tardi possibile prima di partire sul [per il ] viaggio

What does “it” refer to? It is a little ambiguous.

In this case, the 'it' refers to the act of departing and is a common construction in English. You'll see it in similar phrases such as "Don't leave it until the last minute to post your Christmas cards." Here, the 'it' is the act of posting the cards. The same sentence could be rewritten thus: "Don't leave posting your Christmas cards until the last minute" or "Don't wait until the last minute to post your Christmas cards".

Of all the questions it was the least difficult
Di tutte le domande era la meno difficile

Tim was the least nervous in the team
Tim era il meno nervoso della squadra
I’m good at drawing so Art is the least difficult school subject for me
Sono bravo a disegnare, perciò arte è la material (scolastica) meno difficile per me